Those verses are not clear on who,"whom" is.<quoted text>
Being the greatest and being Christ's favorite may not be strictly synonymous but I think it is a fair assumption.
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When Jesus therefore saw his mother, and the disciple standing by, whom he loved, he saith unto his mother, Woman, behold thy son!
One of them, the disciple whom Jesus loved, was reclining next to him.
The below commentary explains why this is believed to be the apostle John
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